Question

A school had an election where the candidates received votes in the ratio of 1:2:3. If the winning candidate received 210 votes, how many people voted in the election?

Answer 1

Now, let's say the total of folks voting were "x".

now, if we divide "x" even into "1+2+3" pieces, we'd get some quotient value, the first candidate took 1 of those even pieces, the second candidate took 2 of those even pieces, and the winning candidate took 3 of them, thus winning anyway.

let's do the division, keeping in mind that the winning candidate had 210 votes.

$\bf \cfrac{x}{1+2+3}\implies \cfrac{x}{6}\implies \stackrel{\textit{winning candidate pieces}}{3\cdot \cfrac{x}{6}}=\stackrel{\textit{winning candidate votes}}{210} \\\\\\ \cfrac{3x}{6}=210\implies \cfrac{x}{2}=210\implies x=420$